Boltzmann legacy and wealth distribution

TL;DR

This paper reviews kinetic equations modeling wealth distribution among agents, highlighting how mathematical techniques reveal the emergence of Pareto tails and the relaxation process to equilibrium.

Contribution

It applies kinetic theory methods to analyze wealth distribution models, elucidating the formation of Pareto tails and the dynamics of wealth evolution.

Findings

Identification of interaction rules leading to Pareto tails

Analysis of relaxation to stationary wealth profiles

Application of kinetic theory techniques to economic models

Abstract

We briefly review results on nonlinear kinetic equation of Boltzmann type which describe the evolution of wealth in a simple agents market. The mathematical structure of the underlying kinetic equations allows to use well-known techniques of wide use in kinetic theory of rarefied gases to obtain information on the process of relaxation to a stationary profile, as well as to identify simple interaction rules which are responsible of the formation of Pareto tails.